Close F. Particle Physics: A Very Short Introduction

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Energy is profoundly linked to temperature also. If you have a vast

number of particles bumping into one another, transferring energy

from one to the next so that the whole is at some ﬁxed temperature,

the average energy of the individual particles can be expressed in eV

(or keV and so on). Room temperature corresponds to about 1/40

eV, or 0.025 eV. Perhaps easier will be to use the measure of

1 eV

K (where K refers to Kelvin, the absolute measure of

temperature; absolute zero 0K = −273 Celsius, and room

temperature is about 300 K).

Fire a rocket upwards with enough energy and it can escape

the gravitational pull of the Earth; give an electron in an atom

enough energy and it can escape the electrical pull of the

atomic nucleus. In many molecules, the electrons will be

liberated by an energy of fractions of an eV; so room

temperature can be sufﬁcient to do this, which is the source

of chemistry, biology, and life. Atoms of hydrogen will survive

at energies below 1 eV, which in temperature terms is of the

order of 10

K. Such temperatures do not occur normally on

Earth (other than speciﬁc examples such as some industrial

furnaces, carbon arc lights, and scientiﬁc apparatus) and so

atoms are the norm here. However, in the centre of the Sun, the

temperature is some 10

K, or in energy terms 1 keV; atoms cannot

survive such conditions.

At temperatures above 10

K there is enough energy available that

it can be converted into particles, such as electrons. An individual

electron has a mass of 0.5 MeV/c

, and so it requires 0.5 MeV of

energy to ‘congeal’ into an electron. As we shall see later, this cannot

happen spontaneously; an electron and its antimatter counterpart –

the positron – must be created as a pair. So 1 MeV energy is needed

for ‘electron positron creation’ to occur. Analogously, 2 GeV energy

is needed to create a proton and its antiproton. Such energies are

easy to generate in nuclear laboratories and particle accelerators

today; they were the norm in the very early universe and it was in

those ﬁrst moments that the basic particles of matter (and

Particle Physics

4. The correspondence between scales of temperature and energy in

electronvolts (eV).

antimatter) were formed. The details of this will be given in

Chapter 9, but some outline will be useful for orientation now.

The galaxies are observed to be rushing apart from one another

such that the universe is expanding. From the rate of the expansion

we can play the scenario back in time and deduce that about 14

billion years ago the universe would have been compacted in on

itself. It is the explosive eruption from that dense state that we call

the Big Bang. (It is not the primary purpose of this book to review

the Big Bang; to learn more read Peter Coles’ Cosmology in the Very

Short Introduction series). In that original state, the universe

would have been much hotter than it is now. The universe today is

bathed in microwave radiation with a temperature of about 3 K.

Combining this with the picture of the post-Big Bang expansion

gives a measure of temperature of the universe as a function

of time.

Within a billionth of a second of the original Big Bang, the

temperature of the universe would have exceeded 10

K, or in

energy terms 1 TeV. At such energies particles and antiparticles

were created, including exotic forms no longer common today. Most

of these died out almost immediately, producing radiation and

more of the basic particles such as electrons and the surviving

quarks that make up matter today.

As the universe aged, it cooled, at ﬁrst very quickly. Within a

millionth of a second quarks clustered together in threes, where

they have remained ever since. So protons and neutrons were born.

After about three minutes the temperature had fallen to about 10

K, or in energy 1 MeV. This is ‘cool’ enough for protons and

neutrons to stick together and build up the nuclear seeds of the (yet

to be completed) atomic elements. A few light nuclei were formed,

such as helium and traces of beryllium and boron. Protons, being

stable and the simplest, were most common and clustered under

gravity into spherical balls that we call stars. It was here that the

nuclei of heavy elements would be cooked over the next billions of

Particle Physics

years. In Chapter 9 I shall describe how the protons in these stars

bumped into one another, clustering together and by a series of

processes made the nuclear seeds of heavier elements: ﬁrst helium,

and eventually the heavier ones such as oxygen, carbon, and iron.

When such stars explode and die they spew these nuclear seeds out

into the cosmos, which is where the carbon in your skin and the

oxygen in our air originated.

The Sun is going through the ﬁrst part of this story now. It has been

converting protons into the nuclei of helium for 5 billion years and

has used up about half of its fuel so far. The temperatures involved

in its heart that do this are similar to those of the whole universe

when it was a few minutes old. So the Sun is carrying on today what

the universe did at large long ago.

Atoms cannot survive inside the depths of the Sun, and nor could

they in the early universe. It was not until some 300,000 years had

elapsed that the universe had cooled enough for these nuclei to

entrap passing electrons and make atoms. That is how things are

here on Earth today.

How big and small are big and small?

Chapter 3

How we learn what things

are made of, and what

we found

Energy and waves

To ﬁnd out what something is made of you might (a) look at it; (b)

heat it and see what happens; or (c) smash it by brute force. There is

a common misconception that it is the latter that high-energy, or

‘particle’, physicists do. This is a term left from the days when

particle accelerators were known as ‘atom smashers’. And indeed,

historically that was what took place, but today the aims and

methods are more sophisticated. We will come to the details later,

but to start, let’s focus on the three options just mentioned. Each of

them shares a common feature: they all use energy.

In the case of heating, we have already seen how temperature and

energy are correlated (10

K 1eV ). Even in looking at things,

energy will turn out to play a role.

You are seeing these words because light is shining on the page and

then being transmitted to your eyes; the general idea here is that

there is a source of radiation (the light), an object under

Instruments such as microscopes and particle accelerators

enable us to extend our vision beyond the rainbow of visible

light, and see into the subatomic microworld. This has

revealed the inner structure of the atom – electrons, nuclear

particles, and quarks.

investigation (the page), and a detector (your eye). Inside a full stop

are millions of carbon atoms and you will never be able to see the

individual atoms even with the most powerful magnifying glass.

They are smaller than the wavelength of ‘visible’ light and so cannot

be resolved in an ordinary magnifying glass or microscope.

Light is a form of electromagnetic radiation. Our eyes respond only

to a very small part of the whole electromagnetic spectrum; but the

whole of it can be accessed by special instruments. Visible light is

the strongest radiation given out by the Sun, and humans have

evolved eyes that register only this particular range. The whole

spread of the electromagnetic spectrum is there, as we can illustrate

by an analogy with sound. A single octave of sound involves a

halving of the wavelength (or a doubling of the frequency) from one

note (say the A at 440 Hz) to that of an octave above (the A at 880 Hz).

Similarly for the rainbow: it is an ‘octave’ in the electromagnetic

spectrum. As you go from red light to blue, the wavelength halves,

the wavelength of blue light being half that of red (or equivalently,

the frequency with which the electric and magnetic ﬁelds

oscillate back and forth is twice as fast for blue light as red).

The electromagnetic spectrum extends further in both directions.

Beyond the blue horizon – where we ﬁnd ultraviolet, X-rays, and

gamma rays – the wavelengths are smaller than in the visible

rainbow; by contrast, at longer wavelengths and in the opposite

direction, beyond the red, we have infrared, microwaves, and

radio waves.

We can sense the electromagnetic spectrum beyond the rainbow;

our eyes cannot see infrared radiation but the surface of our skin

can feel it as heat. Modern infrared cameras can ‘see’ prowlers by

the heat they give off. It is human genius that has made machines

that can extend our vision across the entire electromagnetic

range, thereby revealing deep truths about the nature of the

atom.

Our inability to see atoms has to do with the fact that light acts like

How we learn what things are made of

a wave and waves do not scatter easily from small objects. To see a

thing, the wavelength of the beam must be smaller than that thing is.

Therefore, to see molecules or atoms needs illuminations whose

wavelengths are similar to or smaller than them. Light waves, like

those our eyes are sensitive to, have wavelength about 10

−7

m (or put

another way: 10,000 wavelengths would ﬁt into a millimetre). This

is still a thousand times bigger than the size of an atom. To gain a

feeling for how big a task this is, imagine the world scaled up 10

million times. A single wavelength of light, magniﬁed 10 million

times, would be bigger than a human, whereas an atom on this scale

would extend only 1 millimetre, far too little to disturb the long blue

wave. To have any chance of seeing molecules and atoms we need

light with wavelengths much shorter than these. We have to go

far beyond the blue horizon to wavelengths in the X-ray region

and beyond.

X-rays are light with such short wavelengths that they can

be scattered by regular structures on the molecular scale,

such as are found in crystals. The wavelength of X-rays is

larger than the size of individual atoms, so the atoms are

still invisible. However, the distance between adjacent planes

in the regular matrix within crystals is similar to the X-ray

wavelength and so X-rays begin to discern the relative

position of things within crystals. This is known as ‘X-ray

crystallography’.

An analogy can be made if one thinks for a moment of water

waves rather than electromagnetic ones. Drop a stone into still

water and ripples spread out. If you were shown an image of these

circular patterns you could deduce where the stone had been. A

collection of synchronized stones dropped in would create a more

complicated pattern of waves, with peaks and troughs as they

meet and interfere. From the resulting pattern you could deduce,

with some difﬁculty admittedly, where the stones had entered.

X-ray crystallography involves detecting multiple scattered waves

from the regular layers in the crystal and then decoding the

Particle Physics

pattern to deduce the crystalline structure. In this way, the shape

and form of very complicated molecules, such as DNA, have been

deduced.

To resolve the individual atoms we need even shorter

wavelengths and we can do this by using not just light, but

also beams of particles such as electrons. These have special

advantages in that they have electric charge and so can be

manipulated, accelerated by electric ﬁelds, and thereby given

large amounts of energy. This enables us to probe ever

shorter distances, but to understand why we need to make

a brief diversion to see how energy and wavelength are

related.

One of the great discoveries in the quantum theory was that

particles can have wavelike character, and conversely that waves

can act like staccato bundles of particles, known as ‘quanta’.

Thus an electromagnetic wave acts like a burst of quanta – photons.

The energy of any individual photon is proportional to the

frequency (ν) of the oscillating electric and magnetic ﬁelds of

the wave. This is expressed in the form

E = hν

where the constant of proportion, h, is Planck’s constant.

The length of a wave (λ), and the frequency with which peaks pass a

given point, are related to its speed, c, by ν = c/λ. So we can relate

energy and wavelength

E =

and the proportionality constant hc ∼ 10

−6

eV m. This enables us to

relate energy and wavelength by the approximate rule of thumb:

‘1 eV corresponds to 10

−6

m, and so on.

How we learn what things are made of

You can compare with the relation between energy and temperature

in Chapter 2, and see how temperature and wavelength are related.

This illustrates how bodies at different temperatures will tend to

radiate at different wavelengths: the hotter the body, the shorter the

wavelength. Thus, for example, as a current ﬂows through a wire

ﬁlament and warms it, it will at ﬁrst emit heat in the form of

infrared radiation – and as it gets hotter, a thousand degrees or so,

it will begin to emit visible light and illuminate the room. Hot

gases in the vicinity of the Sun can emit X-rays; some extremely

hot stars emit gamma rays.

To probe deep within atoms we need a source of very short

wavelength. As we cannot make gamma-emitting stars in the

laboratory, the technique is to use the basic particles themselves,

such as electrons and protons, and speed them in electric ﬁelds. The

higher their speed, the greater their energy and momentum and

the shorter their associated wavelength. So beams of high-energy

particles can resolve things as small as atoms. We can look at as

small a distance as we like; all we have to do is to speed the particles

up, give them more and more energy to get to ever smaller

wavelengths. To resolve distances on the scale of the atomic nucleus,

−15

m, requires energies of the order of GeV. This is the energy

scale of what we call high-energy physics. Indeed, when that ﬁeld

began in earnest in the early to middle of the 20th century, GeV

energies were at the boundaries of what was technically available.

5. Energy and approximate wavelengths.

Particle Physics

By the end of the 20th century, energies of several hundred GeV

were the norm, and we are now entering the realm of TeV scale

energies, probing matter at distances smaller than 10

−18

m. So when

we say that electrons and quarks have no deeper structure, we can

only really say ‘at least on scales of 10

−18

m’. It is possible that there

are deeper layers, on distances smaller than these, but which are

beyond our present ability to resolve in experiment. So although I

shall throughout this book speak as if these entities are the ultimate

pieces, always bear in mind that caveat: we only know how Nature

operates at distances larger than about 10

−18

Accelerating particles

The ideas of accelerators will be described in Chapter 5, but for the

moment let’s reﬂect a moment on what is required. To accelerate

particles to energies of several tens or hundreds of GeV

requires lots of space. Technology in the mid- to late 20th century

could accelerate electrons, say, at a rate corresponding to each

electron in the beam gaining some tens of MeV energy per metre

travelled. Hence at the Stanford Linear Accelerator Center in

California (SLAC) there is a 3-km-long accelerator which produced

beams of electrons at up to 50 GeV. At CERN in Geneva, the

electrons were guided around a circle of 27 km in length, achieving

energies of some 100 GeV. Protons, being more massive, pack a

bigger punch, but still require large accelerators to achieve their

goals. Ultimately it is the quantum relation between short

distances, the consequent short wavelengths needed to probe

them, and the high energies of the beams that creates this apparent

paradox of needing ever bigger machines to probe the most minute

distances.

These were the early aims of those experiments to probe the heart of

the atomic nucleus by hitting it with beams of high-energy particles.

The energy of the particles in the beam is vast (on the scale of the

energy contained within a single nucleus, holding the nucleus

together), and as a result the beam tends to smash the atom and its

How we learn what things are made of